Lay Question Regarding Compton Scattering

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Jim Lundquist
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From what I understand, a photon of "sufficient" energy will interact with a free electron such that the recoil electron receives part of the energy of the photon, and the scattered photon has a Doppler shift (change in wavelength). If the scattered photon still has "sufficient" energy, Compton scattering of that photon may be repeated. What if the scattered photon has "insufficient" energy? Is there any effect at all? Can a photon's energy be totally dissipated by a series of photon-electron interactions?
 
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Jim Lundquist said:
the scattered photon has a Doppler shift (change in wavelength)
This isn’t a Doppler-shift. The energy of the photon decreases (because it goes to the electron), so the wavelength increases.
Jim Lundquist said:
What if the scattered photon has "insufficient" energy?
Then there was only one Compton scattering event.
 
Replusz said:
Then there was only one Compton scattering event.
There may be only one Compton scattering event, but does that mean that no further interactions between that lower energy (longer wavelength) photon and a free electron can happen...matter becoming, in effect, "transparent" to that scattered photon?